Abstract: In this paper we present a variant of the Accelerated Overrelaxation iterative method (AOR), denoted by modified AOR-like method (MAOR-like method) for solving the augmented systems, i.e., the AOR-like method with three real parameters , and . For special values of , and we get the MSOR-like method, the AOR-like method and the SOR-like method. An equation relating the involved parameters and the eigenvalues of the iteration matrix of the MAOR-like method is obtained. Furthermore, some convergence conditions for the MAOR-like method are derived. This paper generalizes the main results of Li, Li, Nie, and Evans 2004 and Shao, Li, and Li (2007). Numerical examples are presented to show that, for a suitable choice of the involved parameters, the MAOR-like method is superior when compared to the above iterative methods and to the SSOR-like method presented by Zheng, Wang, and Wu (2009).